1. CEC 220 Digital Circuit Design Minterms and Maxterms Monday, January 26 CEC 220 Digital Circuit Design Slide 1 of 11

2. Lecture Outline Monday, January 26 CEC 220 Digital Circuit Design Combining Numbers with Logic Creating Boolean Equations Combinational Logic & Truth Tables Minterm and Maxterm Expansions Slide 2 of 11

3. 1 0 0 0 0 0 = -32  C Combining Numbers with Logic Monday, January 26 CEC 220 Digital Circuit Design A word problem:  The temperature in  C is represented as a 6-bit signed 2’s complement number:  What is the highest temp that can be represented?  What is the lowest temp that can be represented?  The boolean expression (i.e. logic) for freezing (i.e. 0  C) is? 0 1 1 1 1 1 = +31  C 1 0 0 0 0 1 = -31  C Slide 3 of 11

4. Combining Numbers with Logic Monday, January 26 CEC 220 Digital Circuit Design  What is the logic for temp > 15  C?  What is the logic for temp = -1  C?  What is the logic for temp  -30  C? >15 = 16 or 17 or … or 31  -30 = -30 or -31 or -32 Slide 4 of 11

5. Minterm and Maxterm Expansions Minterms Monday, January 26 CEC 220 Digital Circuit Design Consider the circuit f = A+BC BC 0 0 0 1 0 0 0 1 ABC 000 001 010 011 100 101 110 111 f 0 0 0 1 1 1 1 1 For a function of n variables, a product term in which each of the n variables appears once is called a minterm. A SOP expression!! Slide 5 of 11

6. Minterm and Maxterm Expansions Maxterms Monday, January 26 CEC 220 Digital Circuit Design ABC 000 001 010 011 100 101 110 111 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 Slide 6 of 11

7. Minterm and Maxterm Expansions Maxterms Monday, January 26 CEC 220 Digital Circuit Design Recalling that ABC 000 001 010 011 100 101 110 111 1 1 1 0 0 0 0 0 A POS expression!! 0 0 0 1 1 1 1 1 Slide 7 of 11

8. Minterm and Maxterm Expansions Maxterms vs Minterms Monday, January 26 CEC 220 Digital Circuit Design ABC 000 001 010 011 100 101 110 111 Maxterms Minterms Maxterm Expression: Minterm Expression: 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 Slide 8 of 11

9. Minterm and Maxterm Expansions An Example Monday, January 26 CEC 220 Digital Circuit Design abcd 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 f 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 f 0 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 Slide 9 of 11

10. Minterm and Maxterm Expansions An Example Monday, January 26 CEC 220 Digital Circuit Design ABC 000 001 010 011 100 101 110 111 1 1 1 0 1 0 0 1 System A B C f 0 0 0 1 0 1 1 0 Slide 10 of 11

11. Next Lecture Monday, January 26 CEC 220 Digital Circuit Design Truth Table Construction Incompletely Specified Functions Design of Adders and Subtractors Slide 11 of 11